Dsesign of experiment

Hmk – General Factorials. Use =0.05 unless otherwise specified

1. An experiment was run to examine the amount of time it takes to boil a given amount of water on the four different burners of her stove, and with 0, 2, 4, or 6 teaspoons of water. The numbers in parentheses are run order. The results of the design are given below.

Salt (teaspoons)
Burner
0
2
4
6
Right Back
7(7)
4(13)
7(24)
5(15)

8(21)
7(25)
7(34)
7(33)

7(30)
7(26)
7(41)
7(37)
Right Front
4(6)
4(36)
4(1)
4(28)

4(20)
5(44)
4(14)
4(31)

4(27)
4(45)
5(18)
4(38)
Left Back
6(9)
6(46)
7(8)
5(35)

7(16)
6(47)
6(12)
6(39)

6(22)
5(48)
7(43)
6(40)
Left Front
9(29)
8(5)
8(3)
8(2)

9(32)
8(10)
9(19)
8(4)

9(42)
8(11)
10(23)
7(17)

a. Analyze the full model and check for significance
b. Reduce your model
c. Check the adequacy of this model
d. Determine which settings yield the shortest time

2. The yield of a chemical process is being studied. The two most important variables are thought to be the pressure and the temperature. Three levels of each factor are selected, and a factorial experiment with two replicates is performed. The yield data follow:

Pressure

Temperature
200
215
230
150
90.4
90.7
90.2

90.2
90.6
90.4
160
90.1
90.5
89.9

90.3
90.6
90.1
170
90.5
90.8
90.4

90.7
90.9
90.1

a. Analyze the full model and check for significance
b. Reduce your model
c. Check the adequacy of this model
d. Under what conditions would you run the process

3. The percentage of hardwood concentration in raw pulp, the vat pressure, and the cooking time of the pulp are being investigated for their effects on the strength of paper. Three levels of hardwood concentration, three levels of pressure, and two cooking times are selected. A factorial experiment with two replicates is conducted, and the following data are obtained:

Percentage
Cooking
Time
3.0 hrs.